The Liverpool icon, 57, has been in a relationship with the brunette beauty, 35, since late 2013 – a year after he split up with long-term partner Tracy after 25 years of marriage.
Speaking to the Irish Independent, former pop star Anthony – who runs her own production company called Home-run Productions – spoke of her delight at the announcement.
She said: "We've been speaking about it for a long time. We don't feel any different as we always knew we would be together for the long haul.
"When we travel together, Ian always introduces me as his wife. Two weeks ago, I corrected him and said, 'Ian, I'm not your wife.'
"He said: 'Yes, but I want you to be. That is, if you want to be?'"
To which Anthony responded by saying: "There's nothing in this world that would make me happier!"
While she also added that Rush – who has two sons from his previous relationship – said to her brother: "I never knew true happiness until I met Carol."
Speaking about the age gap to the Sunday People, she said: "I have always been a Liverpool fan. I watched Ian play on TV when I was younger. My whole family are Liverpool fans.
“But I don’t see an age gap. I did once or twice when we first got together but I don’t any more. I’m trying to stop my ageing process but I think Ian looks better than ever.”
Rush – who netted 346 goals in 660 games for the Reds – has tipped Jurgen Klopp's side to win the Premier League, despite being knocked off top spot.
He told talkSPORT: "I think Liverpool are better coming from behind.
"When you're top, everyone wants to beat you, but when you're second, I think Liverpool prefer to be in that position.
"I'm very confident, to tell you the truth. Yes, Manchester City have a great manager and a great squad, but there'll be a few ups and downs before the end of the season.
"I just feel with the run-in Liverpool have, we've got Man United out of the way, we've got Everton out of the way.
"If you don't beat Chelsea and Tottenham at home, maybe you don't deserve to win the title, but we've got home support in those games and the other games are all winnable. So I'm quite confident."
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